A262957 -id:A262957 - cp's OEIS frontend

A346590 Decimal expansion of lim_{n->infinity} A262957(n)/A263295(n).

5, 7, 6, 6, 3, 3, 3, 8, 9, 7, 3, 0, 1, 8, 4, 3, 9, 2, 3, 9, 7, 8, 9, 1, 7, 4, 9, 7, 8, 2, 9, 1, 3, 9, 2, 5, 7, 9, 6, 1, 4, 9, 4, 3, 5, 2, 7, 5, 7, 1, 0, 8, 3, 9, 8, 4, 1, 1, 0, 4, 1, 9, 1, 8, 0, 7, 6, 4, 8, 3, 5, 4, 4, 0, 1, 2, 4, 4, 0, 2, 0, 2, 0, 3, 1, 8, 2, 2, 6, 4

Offset: 0

Hugo Pfoertner, Jul 25 2021

See A262957 for more information and references.

			0.5766333897301843923978917497829139257961494352757108398411...

Cf. A262957, A263295.

A263295 Denominators of the n-th iteration of the alternating continued fraction formed from the positive integers, starting with (1 - ...).

Original entry on oeis.org

3, 5, 33, 111, 933, 4913, 50585, 364717, 4460647, 40920133, 580574377, 6472209467, 104581586665, 1373040648769, 24902871413201, 376386726269561, 7573128424949291, 129519388933667493, 2863373356440803473, 54670305859684290279, 1317404009250178503245

Offset: 1

Mohamed Sabba, Nov 20 2015

As n->inf, A262957(n)/a(n) converges to 0.57663338973018...; this number has a surprisingly elegant standard continued fraction representation: [0; 1, 1, 2, 1, 3, 4, 1, 5, 6, 1, 7, 8, ...].

			(1-1/(2+1)) = 2/3, so a(1) = 3;
(1-1/(2+1/(3-1))) = 3/5, so a(2) = 5;
(1-1/(2+1/(3-1/(4+1)))) = 19/33, so a(3) = 33;
(1-1/(2+1/(3-1/(4+1/(5-1))))) = 64/111, so a(4) = 111.

Jinyuan Wang, Table of n, a(n) for n = 1..448

Same principle as A244279 and A244280 - except here we begin with subtraction rather than addition.

Cf. A262957 (numerators).

a(n) = if(n%2==0, s=-1, s=1); t=1; while(n>0, t=n+1+s/t; n--; s=-s); denominator(t=1/t)
vector(30, n, a(n)) \\ corrected by Mohammed Sabba, Dec 22 2015

More terms from Mohamed Sabba, Dec 22 2015

cp's OEIS Frontend

A346590 Decimal expansion of lim_{n->infinity} A262957(n)/A263295(n).

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A263295 Denominators of the n-th iteration of the alternating continued fraction formed from the positive integers, starting with (1 - ...).

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